Excellent post, David.Well first, we need to note that the term "spiritual life" is not found in Scripture. That is part of the problem because we are assigning terms to describe a state. What we do find in Scripture is the transcendent life zoe that is discussed by being made alive in Christ. We also see the wages of sin is death. That is what Adam received when he partook of the fruit. The two contrast each other.
Death in Romans 6:23 is referring to the absence of a relationship with God. A separation from God. Therefore, the life that is found in Christ is the means of restoring a bond, a relationship with God. Adam had that before the fall. At the fall, he experienced, in that day, a spiritual death. The relationship was broken and he needed a savior.
Adam was unique. It is inappropriate to speak of him as 'regenerate' or 'born again' for obvious reasons, but he must, pre-fall, have possessed spiritual life. Spiritual death is outlined in Ephesians 2:1-3, and part of that condition is to be under the wrath of God. Pre-fall, Adam was not under the wrath of God. He was placed in a delightful garden, given all manner of food to eat, given dominion over the earth and permitted to give names to all the animals. He was doing 'good works which God prepared beforehand' which is part of the definition of spiritual life. Genesis 3:8a certainly suggests that God was accustomed to walk in the garden and to have fellowship with the couple. That again is an element of spiritual life (John 14:23).